{"paper":{"title":"Mean Curvature Flow of Arbitrary Co-Dimensional Reifenberg Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Or Hershkovits","submitted_at":"2015-08-13T14:45:52Z","abstract_excerpt":"We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called $k$-dimensional $(\\varepsilon,R)$ Reifenberg flat sets in $\\mathbb{R}^n$. Our results generalize the ones from a previous paper by the author, in which the co-dimension one case (i.e. $k=n-1$) was studied. For $\\varepsilon$ fixed, this class is general enough to include (i) all $C^2$ sub-manifolds (ii) all Lipschitz sub-manifolds with Lipschitz constant less than $\\varepsilon$ (iii) some sets with Hausdorff dimension larger than $k$. The Reifenberg condition, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03234","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}